Q:

What is the LCM of 67 and 17?

Accepted Solution

A:
Solution: The LCM of 67 and 17 is 1139 Methods How to find the LCM of 67 and 17 using Prime Factorization One way to find the LCM of 67 and 17 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here: What are the Factors of 67? What are the Factors of 17? Here is the prime factorization of 67: 6 7 1 67^1 6 7 1 And this is the prime factorization of 17: 1 7 1 17^1 1 7 1 When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 67, 17 1 7 1 × 6 7 1 = 1139 17^1 × 67^1 = 1139 1 7 1 × 6 7 1 = 1139 Through this we see that the LCM of 67 and 17 is 1139. How to Find the LCM of 67 and 17 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 67 and 17 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number. Let’s take a look at the multiples for each of these numbers, 67 and 17: What are the Multiples of 67? What are the Multiples of 17? Let’s take a look at the first 10 multiples for each of these numbers, 67 and 17: First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670 First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 67 and 17 are 1139, 2278, 3417. Because 1139 is the smallest, it is the least common multiple. The LCM of 67 and 17 is 1139. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 121 and 29? What is the LCM of 117 and 98? What is the LCM of 89 and 115? What is the LCM of 141 and 25? What is the LCM of 116 and 90?